From: heltai Date: Wed, 30 Jan 2013 16:57:46 +0000 (+0000) Subject: Fixed docs of step-34. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=b21ec8724f63654469d4d4f904fb73328071426b;p=dealii-svn.git Fixed docs of step-34. git-svn-id: https://svn.dealii.org/trunk@28197 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-34/doc/intro.dox b/deal.II/examples/step-34/doc/intro.dox index 71cfc948e9..420350d0b6 100644 --- a/deal.II/examples/step-34/doc/intro.dox +++ b/deal.II/examples/step-34/doc/intro.dox @@ -1,19 +1,11 @@
-This program was contributed by Luca Heltai. - +This program was contributed by Luca Heltai (thanks to Michael +Gratton for pointing out what the exact solution should have been in +the threedimensional case). -

Warning!

- -The three dimensional solution generated by this example program is -wrong. There is a factor of $1/2$ that appears, and we haven't figured -out where it comes from yet. For the moment this issue is "solved" by -multiplying the wind function in the parameter file by two. - -If you think you have spotted the mistake, please let us know. -

Introduction

Irrotational flow

@@ -666,3 +658,16 @@ files in the current directory and an object of type HyperBallBoundary will then be attached to the triangulation to allow mesh refinement that respects the continuous geometry behind the discrete initial mesh. + +For a sphere of radius $a$ translating at a velocity of $U$ in the $x$ direction, the potential reads +\[ +\phi = -\frac{1}{2}U \left(\frac{a}{r}\right)3 r \cos\theta + +\] see, e.g. J.N. Newman, \emph{Marine Hydrodynamics}, 1977, +pp. 127. For unit speed and radius, and restricting $(x,y,z)$ to lie +on the surface of the sphere, +\[ \phi = -x/2.\] In the test problem, +the flow is $(1,1,1)$, so the appropriate exact solution on the +surface of the sphere is the superposition of the above solution with +the analogous solution along the $y$ and $z$ axes, or \[ \phi = +\frac{1}{2}(x + y + z) \] \ No newline at end of file diff --git a/deal.II/examples/step-34/doc/results.dox b/deal.II/examples/step-34/doc/results.dox index d534ed9800..e4c92e08bb 100644 --- a/deal.II/examples/step-34/doc/results.dox +++ b/deal.II/examples/step-34/doc/results.dox @@ -32,7 +32,7 @@ subsection Exact solution 3d # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. - set Function expression = x+y+z # default: 0 + set Function expression = .5*(x+y+z) # default: 0 # The name of the variables as they will be used in the function, separated # by ','. @@ -76,7 +76,7 @@ subsection Wind function 3d # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. - set Function expression = 2; 2; 2 # default: 0; 0; 0 + set Function expression = 1; 1; 1 # default: 0; 0; 0 # The name of the variables as they will be used in the function, separated # by ','. diff --git a/deal.II/examples/step-34/parameters.prm b/deal.II/examples/step-34/parameters.prm index 5e12caf422..60edd7c35e 100644 --- a/deal.II/examples/step-34/parameters.prm +++ b/deal.II/examples/step-34/parameters.prm @@ -27,7 +27,7 @@ subsection Exact solution 3d # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. - set Function expression = x+y+z # default: 0 + set Function expression = .5*(x+y+z) # The name of the variables as they will be used in the function, separated # by ','. @@ -71,7 +71,7 @@ subsection Wind function 3d # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. - set Function expression = 2; 2; 2 # default: 0; 0; 0 + set Function expression = 1; 1; 1 # The name of the variables as they will be used in the function, separated # by ','.